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Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113)

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Description:The purpose of this monograph, which is aimed at the graduate level and beyond, is to obtain a deeper understanding of Quillen's model categories. A model category is a category together with three distinguished classes of maps, called weak equivalences, cofibrations, and fibrations. Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. The authors' approach is to define the notion of a homotopical category, which is more general than that of a model category, and to consider model categories as special cases of this. A homotopical category is a category with only a single distinguished class of maps, called weak equivalences, subject to an appropriate axiom. This enables one to define ``homotopical'' versions of such basic categorical notions as initial and terminal objects, colimit and limit functors, cocompleteness and completeness, adjunctions, Kan extensions, and universal properties. There are two essentially self-contained parts, and part II logically precedes part I. Part II defines and develops the notion of a homotopical category and can be considered as the beginnings of a kind of ``relative'' category theory. The results of part II are used in part I to obtain a deeper understanding of model categories. The authors show in particular that model categories are homotopically cocomplete and complete in a sense stronger than just the requirement of the existence of small homotopy colimit and limit functors. A reader of part II is assumed to have only some familiarity with the above-mentioned categorical notions. Those who read part I, and especially its introductory chapter, should also know something about model categories.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113). To get started finding Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113), you are right to find our website which has a comprehensive collection of manuals listed.
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Description: The purpose of this monograph, which is aimed at the graduate level and beyond, is to obtain a deeper understanding of Quillen's model categories. A model category is a category together with three distinguished classes of maps, called weak equivalences, cofibrations, and fibrations. Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. The authors' approach is to define the notion of a homotopical category, which is more general than that of a model category, and to consider model categories as special cases of this. A homotopical category is a category with only a single distinguished class of maps, called weak equivalences, subject to an appropriate axiom. This enables one to define ``homotopical'' versions of such basic categorical notions as initial and terminal objects, colimit and limit functors, cocompleteness and completeness, adjunctions, Kan extensions, and universal properties. There are two essentially self-contained parts, and part II logically precedes part I. Part II defines and develops the notion of a homotopical category and can be considered as the beginnings of a kind of ``relative'' category theory. The results of part II are used in part I to obtain a deeper understanding of model categories. The authors show in particular that model categories are homotopically cocomplete and complete in a sense stronger than just the requirement of the existence of small homotopy colimit and limit functors. A reader of part II is assumed to have only some familiarity with the above-mentioned categorical notions. Those who read part I, and especially its introductory chapter, should also know something about model categories.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113). To get started finding Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113)

Homotopy Limit Functors on Model Categories and Homotopical Categories (Mathematical Surveys and Monographs, 113)

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